Least Common Multiple of 6 and 20

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Free LCM Calculator determines the least common multiple (LCM) between 6 and 20 the smallest integer that is 60 that is divisible by both numbers.

Least Common Multiple (LCM) of 6 and 20 is 60.

LCM(6,20) = 60

LCM of 6 and 20

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 6 and 20

LCM of 6 and 20 is 60

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 20. First we will calculate the prime factors of 6 and 20.

Prime Factorization of 6


2 6
3 3
1

Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:

6 = 21×31

Prime Factorization of 20


2 20
2 10
5 5
1

Prime factors of 20 are 2,5. Prime factorization of 20 in exponential form is:

20 = 22×51

Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 20.

LCM(6,20) = 22×31×51
LCM(6,20) = 60

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1, 2, 3, 6

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1, 2, 4, 5, 10, 20

Least Common Multiple of 6 and 20 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 20, than apply into the LCM equation.

GCF(6,20) = 2
LCM(6,20) = ( 6 × 20) / 2
LCM(6,20) = 120 / 2
LCM(6,20) = 60

Properties of LCM 6 and 20

(i) The LCM of 20 and 6 is associative

LCM of 6 and 20 = LCM of 20 and 6

Frequently Asked Questions on LCM of 6 and 20

1. What is the LCM of 6 and 20?

Answer: LCM of 6 and 20 is 60.

2. What are the Factors of 6?

Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.

3. What are the Factors of 20?

Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.

4. How to Find the LCM of 6 and 20?

Answer:

Least Common Multiple of 6 and 20 = 60

Step 1: Find the prime factorization of 6

6 = 2 x 3

Step 2: Find the prime factorization of 20

20 = 2 x 2 x 5

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 60 = 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 6 and 20 is 60.